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Map a Problem to Reveal Opportunities for Solution

By Michael S. Slocum

When a company needs to find a problem’s solution, it is important to consider a comprehensive perspective of the system in question prior to problem solving. Not only must the system boundaries be considered, but also a historic analysis of the decisions that have led to the current predicament. This approach provides a comprehensive framework upon which to base decisions concerning what problem to solve. A powerful technique for achieving these objectives is to create a problem-solution decomposition. The problem solution model is simple to construct and provides a diagrammatic perspective of a system’s problem-solution history.

Diagram the Problem

The diagramming technique is simple. The problem is identified with the “circle p,” a description of the problem used to identify the specifics as shown in Figure 1.

Figure 1: Problem

The transition from the problem to a solution is indicated using the “line-segment arrowhead,” seen in Figure 2.

Figure 2: Transition

The solution is identified by the “circle s,” a description of the solution used to identify the specifics, shown in Figure 3.

Figure 3: Solution

A new problem created by the solution is identified with the “circle p prime,” a description of the secondary problem, seen in Figure 4.

Figure 4: New Problem

A complete problem-solution-problem (PSP) model (shown in Figure 5) represents the full cycle – a problem with a solution that generates a secondary problem. The PSP model also indicates contradictions that become inputs to contradiction theory, which is subset of the Theory of Inventive Problem Solving (TRIZ).

Figure 5: Complete Problem-solution-problem (PSP) Model

“I want a certain S to solve P but I am prohibited by P’.” (It is common for the phrase to need some modification to be completely accurate) The S becomes the improving parameter of a technical contradiction and P’ becomes the degrading parameter. The problem is now ready to be assigned one of the inventive parameters (also from TRIZ) for the S and the P.

The PSP model also provides the opportunity to constrain the system for problem solving at any level. The user needs to select an initiating P and a concluding S (or secondary P). The problem solving then takes place inside the constrained system. The user can move around the limitations and focus problem solving at a higher, more strategic level or a lower, more tactical level.

PSP Model Example

Consider the following:

P = The container’s plastic outer body is too hot to be held.
S = Use an additive in the plastic that reduces thermal conductivity, reducing outer body temperature so that it can be held.
P’= The internal chamber that is used to transfer heat is made from the same material in a blow molding process. A reduction in thermal conductivity, therefore, is detrimental to the container’s primary function of heating the contents quickly.

The problem that needs to be solved in this case is making the container able to be held without the consequential degradation in the thermal conductivity of the plastic. The compromise solution is described in the PSP model above. The innovative solution achieves the solution, S, to the problem, P, without the generation of a secondary problem, P’.

The problem solver could also decide to allow the PSP’ triplet to persist while generating a secondary solution, S’, that resolves the secondary problem, P’. This is an example of constraining the system space to either solve a problem or mitigate its negative effects. The PSP may be integrated into the contradiction syntax as follows: “I want to add a thermal insulator to the plastic to make the outer body able to be held, but I can’t because it will also decrease the thermal conductivity of the internal chamber that is used to heat the contents of the container.”

The ability of the object to be held is the parameter that is improved while heat transfer degrades. The PSP is now prepared to be addressed using TRIZ contradiction theory.


It is possible to map an entire system of problems and solutions using this technique. This is useful for a number of reasons:

  1. Identifies a historical perspective for all problems and solutions in a system
  2. Identifies contradictions in a system (each PSP triplet)
  3. Identifies the proper contradiction syntax for each PSP triplet
  4. Identifies strategic and tactical problem solving opportunities
  5. Constrains problem solving at the required location in the PSP model

With a complete view of a problem and its secondary problems and solution, a company will find moreopportunities for innovative solutions.

About the Author:

Michael S. Slocum, Ph.D., is the principal and chief executive officer of The Inventioneering Company. Contact Michael S. Slocum at michael (at) or visit